Verified answer

lim x→16 (x-16)/(√x -4)

Multiply numerator and denominator by(√x +4) to get

(x-16)/(√x -4)={(x-16)(√x +4)}/{(√x -4)(√x +4)}

={(x-16)(√x +4)}/{(x -16)} =(√x +4)

Hence

lim x→16 (x-16)/(√x -4)=lim x→16 (√x +4)=(√16 +4) =4+4=8

lim x->16 (x - 16)/(√x - 4) = lim x->16 (√x - 4)(√x + 4)/(√x - 4) = 4 + 4 = 8